Action-centered information retrieval

ABSTRACT

The system uses natural language to paths of a transition diagram via answer set programming system and provides: an approach for mapping events described in natural language sources to a logical formalism; and integration of Natural Language Processing and constraint-based reasoning inspired by Reasoning about Actions and Change. The system further uses (a) a non-trivial variant of IR in which sources include sequences of events, and queries are made about the state of the world after such events; (b) the extension of techniques for representing dynamic domains to increase the flexibility of the reasoning processes in the presence of uncertainty; (c) a formalization of the IR task based on action languages; (d) an automated IR procedure based on Answer Set Programming (ASP).

BACKGROUND Information Retrieval

Information Retrieval (IR) is concerned with retrieving documents thatare most likely to fulfill the information need represented by queries.In the traditional IR approach to representing sources, the texts arebroken down into lists of keywords, terms, and other contentdescriptors. When presented with a query, an IR system typicallydetermines the relevance of a document to the query by measuring theoverlap of terms between the query and a particular source.

A number of mature approaches have been developed to improve searchresults using techniques such as temporal ordering, query expansion, andgraph based term weighting, however, these approaches may fail tocapture the deeper semantic meaning of the source as the representationsare constructed using syntactic methods. Work in event-centered IR hasfocused on modeling the content of sources as a graph composed of eventmentions from natural language sources and their temporal relationships;however, the approach does not consider the evolution of the state ofthe world in correspondence to these actions.

Answer Set Programming (ASP) and Reasoning about Actions and Change(RAC)

ASP is a form of declarative programming that is useful inknowledge-intensive applications. Search problems in ASP are reduced tocomputing answer sets of logic programs. As such, ASP is well-suited tothe task of leveraging both event mentions and domain knowledge toautomatically obtain a detailed picture of the scenario. RAC isconcerned with representing the properties of actions. With respect toASP, the approach involves temporal reasoning in situations where somefacts are given and we wish to infer additional facts based on theinformation that we have.

SUMMARY OF THE EMBODIMENTS

The system discussed herein addresses this gap and overcomes theshortcomings of syntactic-based methods. The natural language to pathsof a transition diagram via answer set programming system may provide:

-   -   an approach for mapping events described in natural language        sources to a logical formalism;    -   integration of Natural Language Processing and constraint-based        reasoning inspired by Reasoning about Actions and Change.

The system further uses (a) a non-trivial variant of IR in which sourcesinclude sequences of events, and queries are made about the state of theworld after such events; (b) the extension of techniques forrepresenting dynamic domains to increase the flexibility of thereasoning processes in the presence of uncertainty; (c) a formalizationof the IR task based on action languages; (d) an automated IR procedurebased on Answer Set Programming (ASP).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a path for the sentence “Store owners created jobs afterthey opened new stores.”

FIG. 2 shows the FindMatch algorithm.

DETAILED DESCRIPTION OF THE EMBODIMENTS 1. Natural Language to Paths ofa Transition Diagram Via Answer Set Programming

Natural language understanding is often used in modern InformationRetrieval and Question Answering research. Advancement in these fieldsmay rely in part upon translating information described in naturallanguage sources into models that are well suited to addressingparticular information needs. The system(s) described herein describe anapproach for interpreting natural language descriptions of one or moreevents occurring in a given domain and their effects on the state of theworld through construction of corresponding models that facilitatereasoning for information about events occurring in a particular domain.This system interprets natural language passages that talk about asequence of events. In addition to retaining the sequence, the systemmay employ an understanding of the context in which the events haveoccurred to form a picture of how the state of the world may havechanged as a result In this way, it gains a deeper understanding of themeaning of the events, and can make use of that knowledge in response toa query.

The system may function using knowledge gained by interpreting naturallanguage sources describing sequences of events by leveraging naturallanguage processing techniques and constraint-based reasoning overexisting domain knowledge via Answer Set Programming (ASP). The systemmay assume that domain knowledge exists as constraints using Answer SetProgramming. These constraints may embody a transition diagramdescribing all possible world states of the domain and the actions thattrigger transitions between them. The discussion herein assumes theexistence of knowledge in this form.

Given a natural language source describing a sequence of actions, onetask is to map that sequence and corresponding state information, viainference, to one or more paths in the transition diagram. InformationRetrieval systems may use this approach for document preprocessing suchthat they can reason over the resulting models when faced withinformation needs related to understanding events and their effects onthe domain in which they have occurred. Moreover, this preprocessing maybe leveraged by Question Answering systems to identify more promisingsets of documents from which to extract answers.

1.1. Preliminaries 1.1.1. Syntax and Semantics of ASP

Let Σ be a signature containing constant, function, and predicatesymbols. Terms and atoms are formed as in first-order logic. A literalis an atom a or its strong negation a. Literals are combined to formrules that represent both domain knowledge and event mentions in ourapproach. A rule in ASP is a statement of the form:h₁, ∨ . . . ∨, h_(k)←l₁, . . . , l_(m), not l_(m+1), . . . , notl_(n)  EQ. 1,

where h_(i)'s (the head) and l_(i)'s (the body) are literals and not isthe so-called default negation. Intuitively, the meaning of defaultnegation is the following: “if you believe {l₁, . . . , l_(m)} and haveno reason to believe {l_(m+1), . . . , l_(n)}, then you must believe atleast one of h_(i)'s”. An ASP rule with an empty body is called a fact,and that in writing facts, the ← connective is dropped.

Rules of the form ⊥←l₁, . . . , not l_(n) are abbreviated ←l₁, . . . ,not l_(n), and called constraints, intuitively meaning {l₁, . . . , notl_(n)} must not be satisfied. A rule with variables (denoted by anuppercase initial) is interpreted as a shorthand for the set of rulesobtained by replacing the variables with all possible variable-freeterms.

A program is a set of rules over Σ. A consistent set S of domainliterals is closed under a rule if {h₁, . . . , h_(k)} ∩≠0; whenever{l₁, . . . , l_(m)} ⊆S and {l_(m+1), . . . , l_(n)} ∩S=0. Set S is ananswer set of a not-free program Π w.r.t. S is the minimal set closedunder its rules. The reduct, Π^(s), of a program Π w.r.t. S is obtainedfrom Π by removing every rule containing an expression “not 1” s.t 1 ∈Sand by removing every other occurrence of not 1.

1.2.2 Domain Description

For the formalization of all possible evolutions of the domain overtime, the system may employ techniques from RAC. This formalization iscalled a domain description and represents our domain knowledge. Adomain description is a collection of ASP rules encoding the direct andindirect effects of actions that occur in the domain.

Fluents are first-order terms denoting properties of interest in adomain whose truth value may change over time. For example, opened(s₁,y₁) may represent the fact that store s₁ was opened in the year y₂.A fluent literal is a fluent f or its negation ¬f.

A set A of fluent literals is consistent if ∀f, {f, ¬f} ⊆A and completeif ∀f, {f, ¬f} ∩A≠0. The fact that a fluent f holds at a step i in theevolution of the domain is represented by the ASP atom holds (f, i).Similarly, if f does not hold at step i, we write ¬holds(f, i). Actionsare represented by first-order terms as well. The occurrence of anaction a at step i is represented by an ASP atom occurs (a, i).

The three types of ASP rules used to represent domain descriptions arediscussed next In the following, S is a variable ranging over allpossible steps in the evolution of the domain. Given a fluent literal l,the abbreviation X (l, S) stands for holds (f, S) if l=f, and ¬holds (f,S) if l=¬f. A dynamic (causal) law is a statement of the form:χ(l₀, S+1)←χ(l₁, S), . . . , χ(l_(n), S), occurs (a, S)  EQ. 2,

where a is an action and l_(i)'s are fluent literals. The statementintuitively means that if a is executed in a state in which l₁, . . . ,l_(n) hold, it causes l₀ to hold in the resulting state.

A state constraint is a statement of the form:χ(l₀, S)←χ(l₁, S), . . . , χ(l_(n),|S).  EQ. 3,

where l_(i)'s are fluent literals. The statement says that l₀ holdswhenever l₁, . . . , l_(n) hold.

An executability condition is a statement of the form:←χ(l₁, S), . . . , χ(l_(n), S) occurs (a, S)  EQ. 4,

where a and l_(i)'s are as above. The statement says that action acannot be executed if l₁, . . . , l_(n) hold.

The domain description also contains rules that capture the principle ofinertia, which states that things generally stay as they are. That is tosay that if a fluent is true (or not true) at the current time step, andthere is no reason to believe that the fluent's truth value has changedat the next time step, then we continue to believe that the fluent istrue (resp. not true) in the next time step.holds(F, S+1)←fluent(F), holds(F,S), not ¬holds(F,S+1).¬holds(F,S+1)←fluent(F), ¬holds(F,S), not holds(F,S+1).  EQs. 5, 6

The next rule is called the “awareness axiom” and ensures that areasoner considers both possible cases of any fluent whose initial truthvalue is unknown.holds(F,0) ∨¬holds(F,0)←fluent(F)  EQ.7.

Note that if complete knowledge about the initial state is available inthe problem instance, then the awareness axiom is rendered inapplicable.Both the inertia rules and the awareness axiom represent simple yetpowerful commonsense knowledge that that makes it possible to reasonabout complex effects of actions on fluent literals of the domain.

A set A of fluent literals is closed under a state constraint if eitherl₁, . . . , l_(n)1

A or l₀∈A. A state of a domain description D is a complete andconsistent set of fluent literals closed under the state constraints ofD. Given state σ, h(σ; i) denotes {holds(f, i)|f∈σ} ∪{¬holds (f,i)|¬f∈σ}. Action a is executable in state σiff D∪h(σ, 0)∪{occurs (a, 0)}has at least one answer set.

The set of the possible evolutions of D is represented by a transitiondiagram, i.e., a directed graph τ(D)=<N, E> such that:

1. N is the collection of all states of D;

2. E is the set of all triples <σ, a, σ′> where σ, σ′ are states, a isan action (or event) that is executable in σ, and D∪h(σ, 0)∪{occurs (a,0)} has an answer set, A, such that h(σ′, 1)⊆A.

A sequence <σ₀, α₀, σ₁, . . . , α_(k-1), σ_(k)> is a path of τ(D) ifevery <σ_(i), α_(i), σi+₁> is a valid transition in the graph.

1.3. Mapping Natural Language to Paths of a Transition Diagram

Our approach to interpreting a source is composed of two high-levelsteps: Processing a natural language source, and reasoning about stateinformation in order to enable the construction of a path. In thissection, we will follow the processing of a sample natural languagesource into to a path representing events and information about theireffects on the state of the world. We will consider the following simplesentence to demonstrate the system approach:

“Store owners created jobs after they opened new stores.”

Although multiple valid paths may be identified by the approach, forsimplicity's sake we focus on the construction of a single path for thisexample.

1.4. Processing the Natural Language Source

The first step involves extracting mentions of actions from a naturallanguage source. After collecting the actions, they are placed in achronologically ordered list. Finally, we translate each action into acorresponding logical statement describing the occurrence of the eventat its specific step. For example, if an action is at the first positionin the list, we say that it occurs at time step 0.

1.4.1 Extracting Event Mentions

To extract event mentions from the sources, the system may use syntacticparsing to detect the events. The system parses the source text usingthe Stanford CoreNLP libraries3 which yields tokens, syntacticdependency information, coreference information, and other syntacticattributes of the input text. This information may be used to furtherinterpret the natural language text.

From the syntactic parsing results, the system may extract two kinds ofaction tuples by linking dependencies across the sentence. The first isof the form action, subject/object and represents actions related to asubject or object, but not both (e.g. “stores opened” or “jobs werecreated”). The second is of form action, subject, object and representsactions performed by a subject with respect to some object (e.g. “Storeowners created jobs.” becomes created, owners, jobs ).

Once the system has extracted the action tuples, it uses the coreferenceinformation obtained from the parsing step for anaphora resolution ifneeded. Finally, all verbs are lemmatized to obtain the base forms. Inthe case of our running example, the system returns the tuples(create,owners,jobs) and (opened, owners, stores).

1.4.2 Ordering Event Mentions

The goal of the next step is to store the action predicates in achronologically ordered list Consider a constrained natural languagethat adheres to a specific format for describing sequences of events. Acurrent approach requires that the natural language sources contain asingle sentence conforming to the following template:e1(temporal relation)e2  EQ. 8,

where e1 and e2 are mentions of actions and the temporal relation tag isone of the markers from Allen's interval calculus, specifically BEFOREand AFTER. This marker represents the temporal relationship of events e1and e2. In our example, e1 intuitively maps to the statement that jobswere created by store owners, e2 corresponds to the statement that newstores were opened, and the temporal relation AFTER indicates that thefour new stores opened prior to the creation of the new jobs. We use theresults of the syntactic parsing and the value of the temporal relationin order to construct an ordered list of events. In our example, thesource contains the word “after” which is interpreted to signify thatopened, owners, stores, or e1 from our specification of source format,should appear in the list after create, owners, jobs, or e2. The systemmay incorporate existing temporal relationship extraction systems asmodules that may lift the constraints placed on the format of thesources. The system may also include handling event descriptions inwhich no temporal relationship can be extracted.

1.4.3 Translating to ASP

The system may translate the event mentions to an equivalent ASP formusing syntactic rules, however, work exists on translating naturallanguage directly to ASP using more advanced techniques. NL2KR is asophisticated system for such a translation up to the point of beingable to learn meanings of words that it has not encountered before andmay be used with the system to improve the natural language translationof events to ASP.

Our system first converts the predicate tuples into corresponding ASPform action (subject) or action (actor,target), and writes the ASPpredicates into the problem instance. In our example, we have open(owners,stores) and create (owners,jobs). Finally, we assign occurrencesof the actions to steps based on the ordering, and we encode theinformation by means of occurs (a, i) statements. For the example above,the corresponding facts are:

occurs(open(owners,stores),0).

occurs(create(owners,jobs),1).

1.5. Reasoning About State Information and Path Construction

The second step of the approach involves reasoning over the eventmentions together with the domain and commonsense knowledge in order toidentify paths in the transition diagram consistent with the sources andto determine the corresponding states of the world. As mentionedearlier, we assume the existence of commonsense and domain-specificknowledge.

Knowledge of actions and domain may be combined into a single ASPprogram over which a solver reasons for information about the state ofthe world. In our approach, the problem instance contains the ASP rulescorresponding to action mentions and the problem encoding contains ASPrules corresponding to domain knowledge and common sense. Inference isapplied to the ASP program in order to determine how the effects of theactions are propagated. The product of the reasoning process is acollection of facts about each step in the evolution of the domain. Thisinformation identifies one or more possible paths of the domain'stransition diagram. More precisely, each answer set of the programrepresents a distinct path. The task of finding the corresponding pathsin the transition diagram involves invoking an ASP solver, such asclingo4, to find the answer sets of the logic program. The rules of thedomain description used next may be hand-encoded. The domain descriptionin this example contains commonsense information about the effects ofopening something and the effects of creating something. For example,knowledge of the act of opening a store is represented using thefollowing two rules:fluent(is_open(Y))←occurs(open(X,Y),S).holds(is_open(Y),S+1)←occurs(open(X,Y),S).   EQs. 9, 10

The first rule defines a fluent of the form is_open (Y, X) for everyoccurrence of an action open(X, Y) mentioned by the source 5. The secondrule states that the effect of X opening Y is that Y is open. Knowledgeof the creation of Y by X is similarly encoded by rules stating that, ifX creates Y, then there exists new Y.

To reason about the effects of the actions from our example on the stateof the world with respect to the domain description, the system may feedthe problem instance and problem encoding to the clingo solver. Finally,the system parses the output of the solver and builds a pathrepresenting states of the world at each step of the example and edgesrepresenting events connecting them. The path may be constructed usingthe python NetworkX6 library. The results, shown in Table 1, which showsvalues of domain fluents before, during, and after example events, arequite intuitive once the stores have been opened, they remain open inall subsequent states thanks to the inertia axiom (and unless

otherwise specified by other portions of the source).

TABLE 1 Step Action is open(stores) exists new(jobs) 0 open (owners,stores) false false 1 create (owners, jobs) true false 2 — true true

Similarly, once the jobs are created, they remain in existence insubsequent states as we have no information stating that the jobs havebeen taken. The system additionally displays a graphical representationof the path(s), as shown in FIG. 1 .

1.6. Use Cases

In this section, we present use cases to illustrate the depth ofunderstanding that is achieved in the system. The first use casedemonstrates the necessity of the awareness and inertia axioms tocorrectly assert what is true and what is not in each state along apath. The second illustrates an application in Question Answering.

1.6.1. Use Case 1: Google Acquires Motorola

Here we demonstrate how the system is capable of leveragingcommonsensical axioms, such awareness and inertia, to process naturallanguage sources that describe actions. We show that a detailedprocessing of an example from the literature requires the use of inertiaand awareness. We will begin by processing a natural language source anda domain description that includes both axioms. Then we will observe theloss of quality of the representation when we remove awareness from thedomain description, and then we will observe the further distortion wheninertia is also removed. For this example, we would like to find a paththat corresponds to the following sentence: “Google bought Motorolaafter the government approved the acquisition.”

The domain description contains information about the effects ofpurchasing and approval. Knowledge of the act of purchasing isrepresented using the following two rules:

-   fluent(is owned by(Y,X))←occurs (buy (X,Y),S).-   holds(is owned by(Y,X),S+1)←occurs(buy(X,Y),S).

The first rule defines a fluent of the form is_owned by (Y, X) for everyoccurrence of an action buy (X, Y) encountered in the source. The secondrule states that the effect of X buying Y is that Y is_owned by X.Knowledge of X approving Y is similarly encoded by rules stating that,if X approves Y, then Y is allowed by X.

Given the above sentence and the domain description, our prototype mapsthe sentence to ASP statements as described in the previous section,invokes the clingo solver, and produces the state information shown inTable 2, which shows values of fluents in each state with awareness andinertia in the domain description, and describes actions and theireffects at specific time steps along the path.

TABLE 2 allows is owned by Step Action (acquisition, gov't) (Motorola,Google) 0 approves false false (gov't, acquisition) 1 buy true false(Google, Motorola) 2 — true true

At steps 1 and 2, the value of the fluent is owned by(Motorola, Google)is false, meaning that Google does not own Motorola. However, when theaction buy(Google, Motorola) occurs at step 1, a transition occurs tostep 2 in which Google does own Motorola, i.e. the value of is ownedby(Motorola, Google) is true.

To highlight the importance of the awareness axiom, let us consider theeffects of removing it from the domain description. Table 3 shows thatthere are no truth values for either of the domain fluents until afterthe occurrence of the events that define them.

TABLE 3 allows is owned by Step Action (acquisition, gov't) (Motorola,Google) 0 approves — — (gov't, acquisition) 1 buy true — (Google,Motorola) 2 — true true

That is to say that the value of a fluent is not true or false unlessexplicitly expressed in the domain description or as a result of anaction. The awareness axiom allows the system to make hypotheses aboutthe values of each possible fluent in every state as we saw in Table 2.

When we additionally remove the inertia axiom from the domaindescription, the information that can be inferred about the states ofthe domain is further reduced. Specifically, Google owns Motorola in thestate just after the purchasing action, but the system has noinformation about the ownership in any subsequent states as can be seenin Table 4.

TABLE 4 allows is owned by Step Action (acquisition, gov't) (Motorola,Google) 0 approves — — (gov't, acquisition) 1 buy true — (Google,Motorola) 2 — — true

It is easy to see that both awareness and inertia are crucial to havingaccurate state information that reflects not only domain knowledge buthuman-like intuition about the state of the world when commonsense factsare not explicitly stated.

1.6.2. Use Case 2: John Sells All of His Possessions

In this example, we illustrate how the representation proposed in thisapproach may be used in conjunction with Question Answering techniquesto enhance a QA system's ability to reason for answers that are notexplicitly stated in the sources or the domain knowledge. Finding suchan answer can involve a deeper understanding of both the domain and thescenario in question. Consider the following sentence: “John sold hismost valuable possessions to Mary before he sold his least valuablepossessions to Frank.”

Assume that we have a domain description which contains facts aboutJohn. First, there are definitions of John's valuable and invaluablepossessions. For example, John's house at 123 Lancaster Avenue is listedamong his valuable property. Additional commonsense rules exist in thedescription regarding purchasing and ownership, similar to what we havedemonstrated in previous examples.

Suppose that we would like to know the answer to the question “Whocurrently owns the house at 123 Lancaster Avenue

” Referring to the knowledge base alone, the system would incorrectlyanswer that John owns the house because it is listed among his valuableproperty. However, because we have processed the sentence about Johnselling his possessions, we now have an understanding of the effects ofhis sales on the state of the world. An end-to-end QA system would thenbe able to correctly infer that Mary now owns all of John's valuablepossessions, and because there is no additional information stating thatMary has sold the house, the system could correctly answer that she isthe current owner.

In this section, we discussed a system that takes a non-trivial approachthat extends the state of the art of the event-based documentrepresentation by proposing a rich semantic encoding of events and theconsequences of their occurrence on the state of the world.

2. Information Retrieval with Actions and Change: An ASP-Based Solution

In this section, we begin by analyzing the problem and, appealing tocommonsense and intuition, determining reasonable outcomes of the taskrequired. We use toy examples, which we progressively elaborate, but theapproach easily applies to more practical cases. Later, we developneeded systemically logical foundation and machine learning. It shouldbe noted that we assume that passages in natural language have alreadybeen translated into a suitable logic form. Let us start from thefollowing:

Example 1

The user's query, Q, is “Is John married

” Available information sources are:

S1: “John went on his first date with Mary.”

S2: “John read a book.”

We want to determine which source is most relevant to Q.

The query refers to the current state of the world, which with someapproximation we can identify with the final state of the world in thesources. The sources describe events that occurred over time. Neithersource mentions being married, making syntactic-based methods unfit forthe task. However, from an intuitive perspective, S1 is more relevant toQ than S2. In fact, S1, together with commonsense knowledge that marriedpeople (normally) do not go on first dates, provides a strong indicationthat John is not married. S2, on the other hand, provides no informationpertaining the query.

In this simple example, one can not only identify S1 as the mostrelevant source, but also obtain an accurate answer to the question. Thesimplicity of the example blurs the line between IR and questionanswering. In general, however, providing an accurate answer requires asubstantial amount of reasoning to be carried out once a relevant sourcehas been identified, as well as deep understanding of the content of thesource and a large amount of world knowledge—something that is stillchallenging for state-of-the-art approaches. We focus on definingtechniques that provide the reader with a ranking of the sources basedon our expectation that answers may be found in them.

To focus on the core IR task, we assume that query and sources havealready been translated to a temporally-tagged logical representation.We also assume the availability of suitable knowledge repositories. Itshould be noted that, while our work is somewhat related to research ontemporal relations (e.g., Allen's interval calculus), the two differbecause we focus on reasoning about events and their effects, ratherthan relations between events.

2.1. Preliminaries

The system in this section 2 builds upon action language AL for therepresentation of knowledge about actions and their effects. The syntaxof AL builds upon an alphabet consisting of a set F of symbols forfluents and a set A of symbols for actions. Fluents are booleanproperties of the domain, whose truth value may change over time. Afluent literal is a fluent f or its negation ¬f. The statements of ALare:a causes l₀ if l₁, l₂, . . . , l_(n)   EQ. 11l₀ if l₁, . . . , l_(n)   EQ. 12a impossible if l₁, . . . , l_(n)   EQ. 13

(11) is a dynamic (causal) law, and intuitively says that, if action ais executed in a state in which literals l₁, . . . , l_(n) hold, thenl₀, the consequence of the law, will hold in the next state. (12) is astate constraint and says that, in any state in which l₁, . . . , l_(n)hold, l₀ also holds. (13) is an executability condition and says that acannot be executed if l₁, . . . , l_(n) hold. A set of statements of ALis called action description. The semantics of AL maps actiondescriptions to transition diagrams. A set S of literals is closed undera state constraint (2) if {l₁, . . . , l_(n)}

S or l₀∈S. S is consistent if, for every f∈F, at most one of f, ¬f is inS. It is complete if at least one of f, ¬f is in S. A state of an actiondescription AD is a complete and consistent set of literals closed underthe state constraints of AD.

Given an action a and a state σ, the set of (direct) effects of a in σ,denoted by E(a, σ), is the set that contains a literal l₀ for everydynamic law (1) such that {l₁, . . . , l_(n)} ⊆σ. Given a set S ofextended literals and a set Z of state constraints, the set, CnZ(S), ofconsequences of S under Z is the smallest set of extended literals thatcontains S and is closed under Z. Finally, an action a is non-executablein a state σ if there exists an executability condition (3) such that{l₁, . . . , l_(n)} ⊆σ. Otherwise, the action is executable in σ.

The semantics of an action description AD is defined by its transitiondiagram τ (AD), a directed graph (N, E) such that: N is the collectionof all states of AD, and E is the set of all triples (σ, a, σ¹) where σ,σ¹ are states, a is an action executable in σ, and σ¹ satisfies thesuccessor state equation σ¹=Cn_(z)(E(a, σ)∪(σ∩σ¹)), where Z is the setof all state constraints of AD. Triple (σ, a, σ¹) is called a transitionof τ (AD) and σ¹ is a successor state of σ (under a). A path in atransition diagram T (A) is a sequence ((σ₀, a₀, σ₁, a₁, σ₂, . . . ,σ_(n)) in which every triple (σ_(i), a_(i), σ_(i+1)) satisfies thesuccessor state equation. We denote the initial state of a path π byπ_(σ( )).

Next, we introduce ASP. Let Σ be a signature containing constant,function and predicate symbols. Terms and atoms are formed as infirst-order logic. A literal is an atom a or its negation ¬a. A rule isa statement of the form: h₁, . . . , h_(k)←l₁, . . . , l_(m), notl_(m+1), . . . , not l_(n) where h_(i)'s and l_(i)'s are literals andnot is called default negation operator. Its intuitive meaning in termsof a rational agent reasoning about its beliefs is “if you believe {l₁,. . . , l_(m)} and have no reason to believe {l_(m+1), . . . , l_(n)},then you must believe one of {h₁, . . . , h_(k)}.” If m=n=0, symbol←isomitted and the rule is a fact Rules of the form ⊥←l₁, . . . , l_(n) areabbreviated←l₁, . . . , not l_(n), and called constraints, intuitivelymeaning that {l₁, . . . , not l_(n)} must not be satisfied. A rule withvariables is interpreted as a shorthand for the set of rules obtained byreplacing the variables with all possible variable-free terms. A programis a set of rules over Σ. A consistent set S of literals is closed undera rule if {h₁, . . . , h_(k)} ∩S≠Øwhenever {l₁, . . . , l_(m)} ⊆S and{l_(m+1), . . . , l_(n)} ∩S=Ø. Set S is an answer set of a not-freeprogram if S is the minimal set closed under its rules. The reduct,Π^(S), of a program Π w.r.t S is obtained from Π by removing every rulecontaining an expression “not 1” s.t. 1 S and by removing every otheroccurrence of not 1. Set S is an answer set of Π if it is the answer setof Π^(S).

2.2. Problem Analysis

The previous example allows us to provide a first high-levelcharacterization of the task we aim to study, as one in which we aregiven a query Q and a collection of sources S₁, . . . , S_(n), and areasked to produce scores s₁, . . . , s_(n) indicating how relevant eachsource is to the task of finding an answer to Q. If we adopt theconvention that 0 is the best possible score and ∞ the worst, then it isconceivable that, in Example 1, S₁ should be assigned a score of 0 andS₂a score of ∞ to indicate complete irrelevance.

As in traditional Information Retrieval (IR), the sources may be rankedbased on their respective score. Both syntactic and semantic aspects mayhave to be taken into considerations in determining scores for thedocuments. Thus, below, we use the term “semantic score” when referringto the score assigned to documents by the techniques herein. It is worthstressing the difference between the task at hand and questionanswering, where the goal is to produce a definitive answer. At the endof the process we consider here, the answer to Q may still be unknown,but there will be reason to believe that careful study by a human of thesources identified as relevant will lead to such answer.

Next, we consider a number of examples and corresponding expectations.Based on the examples, later we propose a formalization of the reasoningprocesses. Example 1 showed that the event of going on a first date maylead us to infer that John is not married. But how can one reach suchconclusion

One option is to reason by cases, and consider two possible views of theworld: one in which John is married at the beginning of the story, andone in which he is not Commonsense tells us that the action 1 of goingon a first date is not executable when married. Hence, the view in whichJohn is initially married is inconsistent with the source. So, weconclude that John must not have been married in the initial state.Given further knowledge that one does not get married on a first date,one can infer that John remains not married after the date. Thus, thesource provides evidence that a reader can use to answer the query.

From a technical perspective, the example highlights the importance ofbeing able to reason by cases, to reason about the executability ofactions, and to propagate the truth of properties of interest over theduration of the story. Note, however, that reasoning by cases issometimes misleading. Consider S₂ from Example 1: reasoning by casesleads to the same two possible initial states. Since reading does notaffect married status, there are two ending states for the story. Thismight be taken as an indication that the source provides some usefulevidence for a reader, but it is clear intuitively that S2 is, in fact,irrelevant. Next, let us consider if, and how, the previous query shouldmatch a more complex document. For the sake of this example, let usassume the existence of a fictitious country C, whose laws allow pluralmarriage.

(From now on, we will use action and event as synonyms.)

Example 2

Q: Is John married

S: John, who lives in country C, just went on his first date with Mary.

In this case, S does not provide useful information towards answering Q.John is from C, where plural marriage is allowed, and knowledge aboutplural marriage yields that being married does not preclude a marriedperson from going on a first date. The example also demonstrates theimportance of reasoning about default statements (statements that arenormally true) and their exceptions. The fact that, normally, marriedpeople do not go on first dates is an instance of a default statement,and an inhabitant of C constitutes an exception to it Similarly to S2from the previous example, reasoning by cases may be somewhatmisleading, as it may suggest that the source provides some evidenceuseful to answering the question. Rather than reasoning by cases, itappears to be more appropriate to state that whether John is initiallymarried is unknown. The lack of knowledge is propagated to the finalstate, given that going on a date has no effect on it in the presentcontext The source is thus irrelevant and should receive a semanticscore of ∞. Note the striking difference in scores between S1 from theprevious example and the current source: it appears that in some casesreasoning by cases is useful, while in others reasoning explicitly aboutlack of knowledge is more appropriate. In the next section, we provide acharacterization of reasoning matching this intuition. Next, weinvestigate the role of the effects of actions.

Example 3

Q: Is John married

S: John, who lives in country C, recently went on his first date withMary. A week later, they tied the knot in Las Vegas.

Obviously, a first indication of relevance can be obtained with shallowreasoning and syntactic matching: “tying the knot” is a synonym of“getting married” and “getting married” and “being married” share enoughsimilarities to make a match likely. However, we are interested in moresophisticated reasoning. In the initial state, John may or may not bemarried due to his country's laws. Similarly to Example 1, John'smarried status persists in the state following the first date. Tying theknot, however, has the effect of making John married in the resultingstate. Hence, S is indeed relevant to Q. Intuitively, its semantic scoreshould be equal to that of S1 from Example 1. This demonstrates theimportance of keeping track of the changes in the truth of the relevantproperties over time. The next example takes this argument one stepfurther.

Example 4

Q: Is John married

S: John recently went on his first date with Mary. A week later, theytied the knot in Las Vegas. A month later, they filed for divorce.

Here, we assume that filing for divorce does not immediately cause thespouses to be divorced. For simplicity of presentation, we adopt a viewin which filing for divorce has a non-deterministic effect: in theresulting state, it is equally likely for the spouses to be married ornot The relevance of S to Q is not as straightforward as in some of theprevious cases. It is indeed true that, at the end of the story, it isunknown whether John is married. On the other hand, the story stillprovides some information pertaining to John's married status—certainly,more than source S2 (“John read a book”) from Example 1 or the sourcefrom Example 2 (“John, who lives in country C, just went on his firstdate with Mary.”).

One way to make a distinction between the two cases is to consider that,if S from Example 4 is provided to a reader, and the reader manages todetermine whether the filing action succeeded (e.g., by gatheringadditional evidence), S will immediately allow the reader to answer Q.Differently from the previous examples, knowing that filing occurred isessential to allowing a reader to answer the question. In conclusion,while S is not as relevant to Q as other sources we have considered, itis still somewhat relevant This will have to be reflected in the scoreassigned to the source, which should be higher than the 0 assigned toS1, but obviously smaller than ∞ because the source is indeed relevant.Next, we propose a formalization that captures the behaviors described.

2.3. Formalization of the Reasoning Task

Our formalization leverages techniques from the research on reasoningabout actions and change, and specifically action language AL,approximated representations, and evidence-based reasoning. Thesetechniques rely on a graph-based representation of the evolution of thestate of the world over time in response to the occurrence of actions.We adopt and expand this approach. Specifically, the system'sformalization enables reasoning explicitly about lack of knowledge.Differently from it, however, we allow a reasoner to reason by caseswhenever needed. This is applied to knowledge about both initial stateand effects of actions. Our approach also leverages evidence-basedreasoning to rule out some of the cases considered. Finally, we adopt ALas the underlying formalism, but expand it for an explicitcharacterization of non-deterministic effects and we allow hypothesizingabout exceptional/atypical circumstances, eventually linking them to therelevance of sources. Differently from AL, our language is defined sothat, in the presence of actions with non-deterministic effects, it ispossible to reason both by cases, and by explicitly characterizing lackof knowledge. The syntax of the resulting language, which we call ALIR,is described next by building on that of AL, followed by its semantics.

In ALIR, we identify a (possibly empty) subset D of F called the set ofdefault fluents. Default fluents are assumed false at the beginning of asequence of events. Additionally, an extended (fluent) literal is eithera fluent literal or the expression u (f), intuitively meaning that it isunknown whether f is true or false. Expression u(f) is called properextended literal. The syntax of dynamic law (1) is extended to allow l₀to be an proper extended literal. If l₀ is a proper extended literalu(f), the law intuitively states that the action affects the truth of fnon-deterministically. The action of filing for divorce from Example 4might be modeled with a dynamic law that has u(married) as itsconsequence.

The semantics of ALIR is obtained by extending the definitions toextended literals as needed.

Specifically, a set S of extended literals is consistent if, for everyf∈F, at most one of f, ¬f, u (f) is in S. It is complete if at least oneof f, ¬f, u(f) is in S. A state of an action description AD of ALIR is acomplete and consistent set of extended literals closed under the stateconstraints of AD.

In this phase of the investigation, we restrict our attention to casesin which every action has at most a single direct non-deterministiceffect, and we disallow concurrent actions. The direct effects ofactions are extended as follows. Given an action a and a state σ, theset of combined (direct) effects of a in σ, denoted by E(a

, σ), coincides with E(a, σ) from AL. The set of positive effects of ain σ, E(a⁺, σ), is the set that contains: (a) a fluent literal l forevery dynamic law (1) such that l₀=l and {l₁, . . . , l_(n)}⊆σ, and (b)a fluent f for every dynamic law such that l₀=u(f) and {l₁, . . . ,l_(n)}⊆σ. Similarly, the set of negative effects of a in σ, E(a⁻, σ), isthe set that contains: (a) a fluent literal l for every dynamic law suchthat l₀=l and {l₁, . . . , l_(n)} ⊆σ, and (b) a fluent literal ¬f forevery dynamic law such that l₀=u(f) and {l₁, . . . , l_(n)} ⊆σ.

Given an action description AD, the edges of the correspondingtransition diagram are given by all triples (σ, a∘, σ′) where σ, σ₁ arestates, a is an action executable in σ, ∘ is one of

, +, −, and σ₁ satisfies the equation:σ¹=Cn_(z)(E(a°, σ)∪(σ∩σ¹))  EQ. 15

When multiple successor states exist for a given σ and a∘, the actiondescription is called nondeterministic.

A dynamic law with a proper extended literal u(f) as its consequence hastwo deterministic counterparts, obtained by replacing its consequence byf and ¬f respectively. A dynamic law with a fluent literal as itsconsequence has a single deterministic counterpart, which coincides withthe law itself. An action description AD has emergent non-deterministicbehavior if there exists a non-deterministic action description AD1,obtained from AD by replacing every dynamic law by one of itsdeterministic counterparts. In the current phase of the investigation,we do not consider action descriptions with emergent non-deterministicbehavior.

Next, we turn our attention to the use of transition diagrams to reasonabout sequences of actions and to determine the relevance of availablesources.

2.4 Reasoning about Relevance of Sources

In our approach, a qualified action sequence is a tuple s=<a₀/q₀, a₁/q₁,. . . , a_(k)/q_(k)>i where a_(i)'s are actions and each q_(i) is one of

, ×. Intuitively, qualifier

specifies that the combined effects of the action should be considered,while × indicates that reasoning by cases should be used. The length ofs is k+1. The degree of s, denoted by |s|, is the number of expressionsof the form ai/× in s. If

=<a₀, a₁, . . . , a_(k) 22 is a sequence of actions, we say thats=<a₀/q₀, a₁/q₁, . . . a_(k)/q_(k)> extends

for every possible choice of qualifiers.

denotes the extension of

where all qualifiers are

and

× denotes the extension where all qualifiers are ×. Let σ be a state ands be a qualified action sequence. A path π=<σ₀, α₀, σ₁, . . . , α_(k),σ_(k+1)> is a model of σ, s if all of the following hold: (a) σ₀=σ, (b)if q_(i)=

, then α_(i)=a_(i) ^(?), (c) if qi=×, then α_(i)=a_(i) ⁺ or α_(i)=a_(i)⁻.

Given a set Σ of states and a qualified action sequence s, a path π is amodel of Σ, s if π is a model of σ, s for some σ∈Σ. To illustrate thesenotions, consider an action description {a1 causes ¬g if g; a2 causesu(f) if ¬g}. Let σ be {¬f, g}. It is not difficult to see that the pairσ, <a₁/

, a₂/

> has a unique model, h{¬f, g},

, {¬f, ¬g},

, {u(f), ¬g}i. On the other hand, σ, <a₁/

, a₂/×> has two models, h{¬f, g},

, {¬f, ¬g},

,{f, ¬g}i and {¬f, g},

, {¬f, ¬g},

,{¬f, ¬g}i. The degrees of the two qualified action sequences are 0 and1 respectively.

Let us now consider cases in which knowledge about the initial state isincomplete. Intuitively, if the truth value of f is unknown, one mayassume that f is false if it is a default fluent and that u(f) holdsotherwise. However, as highlighted in the above examples, it issometimes necessary to consider other options for certain fluents. Thisintuition is captured by the notion of forcing of a fluent Given aconsistent set I of extended literals and a fluent f, I[f] denotes theset I defined as follows, called the forcing of f in I: if f∈D and {¬f,u(f)} ∩I=Ø, then I={I∪{f}}; if f∉D and {f, ¬f, u(f)}∩I=Ø, then I={I∪{f}, I∪{¬f}}; otherwise, I={I}. For sets of fluents, the forcing of{f₁, . . . ,f_(m)} in I, written I[{f₁, . . . , f_(m)}], is defined asfollows: (a) if m=1, then I[{f₁}]=I[f₁]; (b) if m>1, then I[{f₁, . . . ,f_(m)}]={I′[f m]|I′∈I[{f₁, . . . , f_(m−1)}]}.

(Action description {q if ¬r, p; r if ¬q, p; a causes p} has an emergentnon-deterministic behavior.)

As an example, let us apply these definitions to S1 from Example 1,“John went on his first date with Mary.” Assume that the translationfrom natural language yields Q=m, F={m, ab}, D={ab}, I=Ø and

=(d). Let us also assume that the action description, AD, is {impossibled if m, ¬ab}.4 Note the use of default fluent ab to formalize the factthat the action is normally impossible if one is married. It is notdifficult to see that I [F\D]=I[{m, ab}\{ab}] is {{m}, {¬m}}, indicatingthat, in the initial state, we can assume that he may or may not havebeen married.

Let Z be the set of state constraints of AD. The default closure of I isthe set δ(I)=C_(nZ)(I∪{¬f|f∈D∧f/∈I}). If δ(I) is consistent, we say thatthe completion of I is the set of extended literalsγ(I)=δ(I)∪{u(f)|f∉δ(I)∧¬f∉δ(I)}. Note that γ(I) may not exist, as in thecase of I={p, q} and of AD={¬q if p}. If γ(I) exists, it is complete,consistent and includes I. Given a set F of fluents, the completion of Iw.r.t F is the set γ(I, F)={γ(I′)|I′∈I|F|∧γ(I′) exists}. The degree ofγ(I, F), denoted by |γ(I, F)|, is |F|.

Going back to Example 1, applying the closure to each element of I[F\D]yields, respectively, {m, ¬ab} and {¬m, ¬ab}, which can intuitively beviewed as the initial states that are consistent with assumptions madeabout m.

As demonstrated by Example 1, there are cases in which the truth ofcertain fluents in the initial state can be inferred indirectly from thesource. The following definition of p(I,

) captures this idea. Given a consistent set I of extended fluentliterals and a sequence of actions

:

$\begin{matrix}{{\rho\left( {I,\aleph} \right)} = {\bigcap\limits_{I^{\prime} \in {l{\lbrack{F\backslash D}\rbrack}}}\left\{ {{I^{\prime}❘{\gamma\left( I^{\prime} \right)}},{\aleph^{x}\mspace{14mu}{has}\mspace{14mu} a\mspace{14mu}{model}}} \right\}}} & {{EQ}.\mspace{14mu} 16}\end{matrix}$

(We use abbreviations to save space. Fluents: m—John is married; ab—Johnis an exception w.r.t going on first dates when married. Actions:d—going on a first date; r—reading a book. In practice, variables may beintroduced to increase generality.)

Note that ρ(I,

) may not exist, e.g., if γ(I1) does not exist for any element ofI[F\D]. If ρ(I,

) does not exist, then the source is irrelevant and its semantic scoreif ∞. If, instead, ρ(I,

) exists, it is not difficult to see that I⊆ρ(I,

).

Let us see how ρ(I,

) is calculated in Example 1. The first step consists in checking formodels of γ(I1),

^(x). Clearly, {m, ¬ab}, (d) has no model, because d is not executable.On the other hand, {¬m, ¬b}, (d) has a model. Hence, ρ(I,

) is the intersection of the only set {¬m}, resulting in ρ(I,

)={¬m}. Intuitively, this mirrors the intuition that John is not marriedin the initial state.

We are now ready to introduce the notion of entailment and to use it todetermine whether there is a match between Q and S. A path π=((σ₀α₀, σ₁,. . . , α_(k−1), σ_(k)) entails a fluent literal l (written π|=l) ifl∈σ_(k). Given a fluent f, we say that π entails ±f (written π|=±f) ifπ|=f or π|=¬f.

For simplicity, we assume Q to be a fluent Let I be a set of fluentliterals explicitly stated to hold in the initial state by S and let

=(a₀, a₁, . . . , a_(k)) be the sequence of actions from S. We say thatS is a match for Q if there exist a set F of fluents and a qualifiedaction sequence s extending

s.t:

c1 π entails ±Q for some model π of γ(ρ(I,

), F), s, and

c2 for every model π′ of γ(π_(σ0)\ρ(I,

), Ø), < >, one of the following holds: (a) π′|≠±Q, or (b)π1|−¬Q andπ′=Q, or (c) π′|=Q and π|=¬Q.

The first condition checks whether the document is relevant to the query—possibly under some assumptions about the default fluents—while thesecond condition ensures that such assumptions are not directly andsolely responsible for the fact that the document is relevant.

The semantic score of S is the smallest value of |γ(ρ(I,

), F)|+|s| for all possible choices of F and s satisfying the aboveitems. If no F and s were found to satisfy the above conditions, then Sis not a match for Q (i.e., it is irrelevant to the query) and itssemantic score is ∞.

In reference to Example 1, let us first look for F , s, satisfying (c1).Let us begin with F=Ø, s=

, which have a degree of 0. It is not difficult to see that γ(ρ(I,

), F)=γ({¬m}, Ø))={{¬m, ¬ab}} and that {{¬m, ¬ab}},

has a unique model π=({¬m, ¬ab},

, {¬m, ¬ab}). Thus, the model entails ±Q, which means that condition(c1) for establishing a match is satisfied.

Next, we check condition (c2). Clearly, γ(π_(σ0)\ρ(I,

), Ø)={{u(m), ¬ab}}. {{u(m), ¬ab}}, < > has a unique model, ({u(m),¬ab}), and it does not entail ±Q. Intuitively, this means that theassumption made about the initial state is not directly responsible forthe ability to entail the query in (c1). Hence, S matches Q.Additionally, because F=Ø, s=

yield a score of 0, the semantic score of the document is 0.

The next possible options, with a combined degree of 1, are F=Ø,s=<r>^(×) and F={m}, s=

. In the first case, there are two models, e.g., π=({u(m), ¬ab}, r⁺,{u(m), ¬ab}), but neither entails ±Q. The second case is moreinteresting. Clearly, there are two models of γ(ρ(I,

), F), s=γ(Ø, {m}),

: π=({m, ¬ab}, r

, {m, ¬ab}) and π=({¬m, ¬ab},

, {¬m, ¬ab}), and π|=Q, while π1|=¬Q. Hence, we need to check condition(c2) for each. For the former, γ(πσ0\Ø, Ø)={{m, ¬ab}}, and {{m, ¬ab}},< > has a unique model ({m, ¬ab}), which entails Q. Thus, the conditionis not satisfied. For π¹, we obtain a unique model ({¬m, ¬ab}), whichentails ¬Q, failing to satisfy the condition as well. Therefore, none ofthese choices for F and s yields a match. Similar conclusions can bedrawn for the other choices for F and s. Hence, S2 does not match Q andreceives a semantic score of ∞. The other examples are solved similarly.The details are omitted to save space, but we provide highlights of someof them.

Example 2. Contrast the previous case with Example 2. People fromcountries that allow plural marriage are exceptions to the custom aboutfirst dates, and thus I={ab},

=(d), and I[F\D]={{m, ab}, {¬m, ab}}. Differently from the previouscase, both sets of I[F\D] yield a model, since ab makes theexecutability condition inapplicable. Hence, ρ(I,

)={ab}. Selecting F=Ø, s=(d)

yields a unique model ({u(m), ab},

, {u(m), ab})|≠±Q. Selecting F={m}, s=

yields two models entailing Q and ¬Q respectively, but the same areentailed by γ(π_(σ0)\ρ(I,

), Ø), < >, thus failing condition (c2). Similar reasoning applies tothe other cases. Because no F, s could be identified, the semantic scoreof S is ∞, indicating that it is irrelevant to Q. Note the key roleplayed by condition (c2) in this example: without it, the source wouldhave been deemed relevant to the query.

Example 4. Consider Example 4, where the action description is expandedwith {w causes m; fd causes u(m)} and relevant executability conditions.We have I=Ø,

=(d, w, fd), and, similarly to Example 1, ρ(I,

)={¬m}. The model obtained from F=Ø, s=

does not entail ±Q. On the other hand, F=Ø, s=(d/

, w/

, fd/×), yield two models, entailing Q and ¬Q resp., depending on theoutcome of fd. This time, condition (c2) is satisfied, since, in bothcases, γ(π_(σ0)\ρ(I,

), Ø)={{u(m), ¬ab}} and {{u(m), ¬ab}}, 0 does not entail ±Q. Inconclusion, S indeed matches Q, and the source has semantic score|Ø|+|(d/

w/

, fd /×)|=1. As expected, its semantic score is worse than that of,e.g., S₁, while obviously better than that of, e.g., S₂.

2.5 Automating the Reasoning Task

Next, we automate the reasoning task discussed earlier by means of atranslation of ALIR to ASP. Given a set I of extended fluent literals, aset F of fluents, a qualified action sequence s, and an actiondescription AD, the encoding of AL_(IR) is program Π_(AD) (I, F, s),described next

In the following, I ranges over steps in the evolution of the domain;given fluent literal l, χ(l, I) stands for holds (f, I) if l=f and¬holds(f, I) if l=¬f. For every action a, the translation includes arule pos(a, I) ∨ neg(a, I)←occurs (a, I), split(a, I). The translationof a dynamic law (1) depends on the form of l₀. If l₀ is a fluentliteral, translation is: χ(l₀, I+1)←occurs (a, I), χ(l₁, I), . . . ,χ(l_(n), I). If l₀ is of the form u(f), the translation of the law is:u(f, I+1)←occurs(a, I), χ(l₁, I), . . . , χ(l_(n)I), not split(a, I).χ(f, I+1)←pos(a, I), χ(l₁, I), . . . , χ(l_(n), I).χ(¬f, I+1)←neg(a, I), χ(l₁, I), . . . , χ(l_(n), I).  EQs. 17, 18, 19

Expression occurs (a, I) states that action a occurs at step I in thestory; split(a, I) states that reasoning by cases should be applied tothe outcomes of that occurrence of a. A state constraint (2) istranslated as an ASP rule of the form holds (l₀, I)←holds (l₁, I), . . ., holds(l_(n), I). Executability condition (3) is translated as arule←occurs(a, I), χ(l₁,I), . . . , χ(l_(n), I). The translation of anaction description is completed by the inertia axioms, which areexpanded in ALIR to accommodate extended literals (F is a variableranging over all fluents):χ(F, I+1)←χ(F, I), not χ(¬F, I+1), not u(F, I+1).χ(¬F, I+1)←χ(¬F, I), not χ(F, I+1), not u(F, I+1).u(F, I+1)←u(F,I), not χ(F, I+1), not χ(¬F, I+1).  EQs. 20, 21, 22

The next axioms define the completion of the initial state:[g₁] χ(F,0)←init(F), χ(¬F, 0)←¬init(F). [g₁][g₂] χ(F,0)←forced(F), default(F), not ¬init(F), χ(F, 0)∨χ(¬F,0)←forced(F), not default(F), not init(F), not ¬init(F),[g₃ ] χ(¬F, 0)←default(F), not χ(F, 0), u(F, 0)←not default(F), not χ(F,0), not χ(¬F, 0).  EQs. 23, 24, 25

Above, statement default (f), included as fact for every f∈D, statesthat f is a default fluent. init(f) (resp., ¬init (f)) says that f isinitially true (resp., false). forced(f) states that f is part of aforcing. Rules [g1] map the knowledge about the initial state tostatements holds(⋅, ⋅). [g₂] formalizes to the notion of forcing. [g₃]defines the completion.

The next step of the definition of Π_(AD) (I, F, s) is the encoding ofits arguments. For every f∈I (resp., ¬f∈I), Π_(AD) (I, F, s) includes afact init (f) (resp., ¬init (f)). For every f∈F, Π_(AD) (I, F, s)includes a fact forced(f). Qualified action sequence s is encoded by aset of facts of the form occurs (a, i) and split(a, i), where a areactions from s and i are their indexes. Specifically,

is translated as a statement occurs(a, i), where i is the index in thesequence, while a^(×) is translated as two facts, occurs(a, i), split(a,i).

This completes the definition of Π_(AD) (I, F, s). Next, we link itsanswer sets to the models of γ(I, F), s. We say that an answer set Aencodes a path π if: (a) for every fluent literal l, l∈σ_(i)iff χ(l, i)∈A; (b) for every fluent f, u(f)∈σ_(i)iff u(f, i) ∈A; (c) for everyaction a, α_(i)=

iff occurs (a,i) ∈A and split(a, i) ∈A; (d) for every action a,α_(i)=a⁺iff {occurs (a, i), split(a, i), pos(a, i)} ⊆A; (e) for everyaction a_(i) αi=a−iff {occurs(a, i), split(a, i), neg(a, i)} ⊆A. Thelink is established by:

Proposition 1

Let I be a consistent set of fluent literals, F be a set of fluents, ands be a qualified action sequence. A path π is a model of γ(I, F), s ifthere exists an answer set of Π_(AD)(I, F, s) that encodes π.

Corollary 1

A model π of γ(I, F), s that entails l exists if there exists an answerset A of Π_(AD)(I, F, s) such that χ(l, k) ∈A, where k is the length ofs. Also, for every fluent f, π|−±f iff {χ(f, k), χ(¬f, k)} ∩A/=Ø.

These results motivate the algorithm in FIG. 2 . Let ∥A∥ be the numberof atoms of A formed by relations forced and split. The behavior of thealgorithm is characterized by Theorem 1: If S is a fluent, then S is amatch for Q iff FindMatch(I,

,Q)≠⊥. The rank of S is ∥FindMateh(I,

,Q)∥.

Inputs to the algorithm:

*I: the set of all fluent literals for which a truth value is known.

*Q, F,

, AD: as described in the paper(s)

DESCRIPTION OF THE ALGORITHM

Step 1 infers which fluent literals are necessarily true or false basedon indirect inference on the information provided. This is accomplishedby calculating ρ(I,

). Specifically, it considers all possible ways of expanding I by makingassumptions about the truth value of non-default fluents from I. Amongthose, it selects the expansions that are compatible with the actions in

. Finally, through an intersection operation it finds the fluentliterals common to all such expansions and assigns such set to variableR.

Step 2 detects cases in which ρ(I,

) does not exist and returns ⊥ to indicate this condition.

Steps 3-7 iteratively consider candidate solutions (F, s), where F is aset of fluents and s is an extension of

, for increasing values of |F|+|s|, i.e. the number of elements in F andthe branching degree of s.

For each candidate solution (F, s), Step 4 checks whether conditions(cl) and (c2) of the definition of the notion “S is a match for Q” hold.Specifically, the step begins by verifying whether the document isrelevant to the query (condition (c1) of the definition of match for Q).To do so, every answer set A that encodes a model of γ(I,F), s isconsidered in turn. Answer sets that do not provide a truth value forthe query Q are discarded. For each remaining answer set A, Step 4acollects the set X of all fluent literals whose truth value in theinitial state had not been already inferred at Step 1.

Step 4b checks condition (c2), i.e. ensures that any assumptions made bythe earlier parts of Step 4 are not directly and solely responsible forthe fact that the document is relevant This is accomplished byconsidering every answer set, B, corresponding to every model of γ(X,Ø)under an empty sequence of actions. For the path encoded by every suchanswer set B, Step 4b checks if the query Q was assumed to be true (orfalse) in the initial state and carried to the final state of the pathwith that truth value by inertia. If this is never the case for any B,then the source has been identified, and Step 4c terminates theexecution of the algorithm.

Otherwise, Step 5 finds a new candidate solution (F′, s′) that has notyet been considered and that is the smallest among all candidatesolutions that are left to be considered.

Step 6 sets (F′,s′) as the current candidate solution and loops back toStep 4.

Proof (sketch). Using the two previous results, the thesis is easilyobtained by observing that step 1 implements the calculation of ρ(I,

), and that steps 4 and 4b check, respectively, conditions (c1) and(c2).

Let us trace the key parts of the algorithm with S₁ from Example 1.Clearly, Π_(AD)(I, F\D,

⊇{←occurs(d, I), holds(m, I), step(I), forced(m), occurs(d, 0).}. Step 1infers the initial truth of fluents indirectly from S₁, resulting in ananswer set containing {¬holds(m, 0), forced(m)}, i.e., John cannot beinitially married. Hence, I₁=I∪{¬m}. Step 4 checks condition (c1). Itresults in a unique answer set A ⊇ {holds(m, 0), ¬holds(ab, 0),occurs(d, 0), ¬holds(m, 1), ¬holds(ab, 1)}, indicating that ({¬m, ¬ab},

, {¬m, ¬ab}) entails ±m. Step 4b checks condition (c2). There is asingle answer set B⊇{u(m, 0), ¬holds(ab, 0), u(m, 1), ¬holds(ab, 1)},and, clearly, {holds(m, 0), ¬holds(m, 0)}∩B=Ø. Hence, (c2) is satisfiedand the algorithm returns A. The rank of S₁ is ∥A∥=0.

3. Applications

The IR system and method herein may be used in search engineoptimization within a wired or wireless network connecting nodes on anetwork of CPUs and storage devices to help identify better answers toqueries, but also in data mining, cybersecurity, healthcare, andbusiness analytics. In each of these areas, the system and method hereinmay define a useful IR approach that can accurately answer queries aboutevents as well as about the state of the world before, during, and afterthe events described in the available sources.

As an overview of the user-process, a user of a computing device (or aclient process) may submit a natural language or other query, which maycontain words or phrases. The query is submitted to the system describedherein. The system searches its corpus of information (database records,documents, web pages, APIs to information systems, etc.), and returnswhat is considered the most relevant results.

Consider an example related to data mining and healthcare: a radiologistmight be looking for information on whether a patient was ever bedriddenfor a period of time. A document reporting that the patient suffered amultiple fracture at his left leg should be returned as relevant, giventhat that the patient was (likely) bedridden as a result of the injury.By linking the event of suffering a leg injury and the resulting stateof the patient, action-centered IR will enable the identification ofsuch a match. Similar considerations can be made for business analytics.An example is related to the role of descriptive analytics in makingretail markdown decisions, where a manager typically wants to examinehistorical data for similar products regarding prices, units sold,advertising, etc. That is, the manager is interested in understandingthe state of the world (e.g., prices and sales) before and afterprevious markdown events—which is exactly what action-centered IR isdesigned for. Finally, in cybersecurity, consider the case of a userasking whether a computer was without network connectivity during acertain timeframe. A system log stating that the router, to which thecomputer is connected, was restarted during that period of time, isindeed a match for the query. However, detecting the match requires anIR technique, such as action-centered IR, capable of observing that arouter restart causes a transition to a state in which all connecteddevices are without connectivity.

While the invention has been described with reference to the embodimentsabove, a person of ordinary skill in the art would understand thatvarious changes or modifications may be made thereto without departingfrom the scope of the claims.

The invention claimed is:
 1. A computer-implemented method ofinformation retrieval (IR), the method to be performed by a network ofprocessors and, comprising: receiving a query; in response to receivingthe query, formalizing event based IR; identifying, using the eventbased IR, sources of information that are relevant to the query, whereinthe event based IR includes at least semantic-level matching in thepresence of sequences of events in the query, and wherein the sources ofinformation at least comprise database records and webpages; verifying,using the event-based IR, that the relevance of the identified sourcesof information is correct; and providing, using the event based IR, theverified sources of information in order of potential relevance to thequery.
 2. The computer-implemented method of claim 1, wherein the eventbased IR provides sources of information relevant to events that occurafter a time relevant to the query.
 3. The computer-implemented methodof claim 2, wherein the event based IR comprises techniques including:Reasoning about Actions and Change (RAC), action language,approximation-based formalization, and evidence based reasoningtechniques.
 4. The computer-implemented method of claim 1, wherein theidentifying step is performed using a sequence of FindMatch (I,

, Q) steps, wherein in response to an input I, wherein I includes fluentliteral explicitly stated to hold in an initial state by S;

is a sequence of actions from S, and Q is a fluent; the FindMatch (I,

, Q) outputs an answer set encoding a path if a match to the queryexists.
 5. The computer-implemented method of claim 4, wherein if S is afluent, then S is a match for Q iff FindMatch(I,

,Q)≠⊥, and a rank of S is ∥FindMatch(I,

,Q)∥.
 6. The computer-implemented method of claim 4, wherein theFindMatch (I,

, Q) steps include the following:
 1. Let R be the intersection of allanswer sets of Π_(AD)(I,

\D,

) and I′ be I ∪ {l| {χ(l, 0), forced(f)} ⊆ R ∧ (l = f ∨ l = ¬f)};
 2. IfΠ_(AD)(I,

\D,

) has no answer set, retain ⊥ and terminate;
 3. Initialize F := ∅ and s:= ϰ^(?);
 4. For every answer set A of Π_(AD)(I′, F, s) such that (χ(Q,k + 1), χ(¬Q, k + 1)} ∩ A ≠ ∅: (a) Let X = {f | holds(f, 0) ∈ A ∧ f ∉I′} ∪ {¬f | ¬holds(f, 0) ∈ A ∧ ¬f ∉ I′}; (b) For every answer set B ofΠ_(AD)(X, ∅, ( )), check that {χ(Q, 0), χ(¬Q, 0)} ∩ B = ∅, or χ(Q, 0) ∈B ∧ χ(¬Q, k + 1) ∈ A, or χ(¬Q, 0) ∈ B ∧ χ(Q, k + 1) ∈ A; (c) If every Bsatisfies the condition, then return A and terminate;
 5. Select a set F′of fluents and an extension s′ of ϰ such that: (a) the pair F′, s′ hasnot yet been considered by the algorithm, and (b) |F′| + |s′| is minimalamong such pairs;
 6. If no such pair F′, s′ exists, then return ⊥ andterminate;
 7. F := F′; s := s′; c Repeat from step
 4.


7. The computer-implemented method of claim 1, wherein the query and thesources of information are in a temporally-tagged logical representationform.
 8. The computer-implemented method of claim 1, wherein the step offormalizing the event based IR is based at least in part on at least oneaction language which is a representation of information on actions andtheir effects corresponding to the event based IR.
 9. Thecomputer-implemented method of claim 8, further comprising automatingthe event based IR by translating from the at least one action languageto at least one answer set corresponding to the query.
 10. A system forinformation retrieval (IR), the system being operable to: receive aquery; in response to the reception of the query, formalize event basedIR; identify, using the event based IR, sources of information that arerelevant to the query, wherein the event based IR includes at leastsemantic-level matching in the presence of sequences of events in thequery, and wherein the sources of information at least comprise databaserecords and webpages; verify, using the event-based IR, that therelevance of the identified sources of information is correct; andprovide, using the event based IR, the verified sources of informationin order of potential relevance to the query.
 11. The system of claim10, wherein the event based IR provides sources of information relevantto events that occur after a time relevant to the query.
 12. The systemof claim 11, wherein the event based IR comprises techniques including:Reasoning about Actions and Change (RAC), action language,approximation-based formalization, and evidence based reasoningtechniques.
 13. The system of claim 10, wherein the identification isperformed using a sequence of FindMatch (I,

, Q) steps, wherein in response to an input I, wherein I includes fluentliteral explicitly stated to hold in an initial state by S;

is a sequence of actions from S, and Q is a fluent; the FindMatch (I,

, Q) outputs an answer set encoding a path if a match to the queryexists.
 14. The system of claim 13, wherein if S is a fluent, then S isa match for Q iff FindMatch(I,

,Q)≠⊥, and a rank of S is ∥FindMatch(I,

,Q) ∥.
 15. The system of claim 13, wherein the FindMatch (I,

, Q) steps include the following:
 1. Let R be the intersection of allanswer sets of Π_(AD)(I,

\D,

) and I′ be I ∪ {l| {χ(l, 0), forced(f)} ⊆ R ∧ (l = f ∨ l = ¬f)};
 2. IfΠ_(AD)(I,

\D,

) has no answer set, retain ⊥ and terminate.
 3. Initialize F := ∅ and s:= ϰ^(?);
 4. For every answer set A of Π_(AD)(I′, F, s) such that (χ(Q,k + 1), χ(¬Q, k + 1)} ∩ A ≠ ∅: (a) Let X = {f | holds(f, 0) ∈ A ∧ f ∉I′} ∪ {¬f | ¬holds(f, 0) ∈ A ∧ ¬f ∉ I′}; (b) For every answer set B ofΠ_(AD)(X, ∅, ( )), check that {χ(Q, 0), χ(¬Q, 0)} ∩ B = ∅, or χ(Q, 0) ∈B ∧ χ(¬Q, k + 1) ∈ A, or χ(¬Q, 0) ∈ B ∧ χ(Q, k + 1) ∈ A; (c) If every Bsatisfies the condition, then return A and terminate;
 5. Select a set F′of fluents and an extension s′ of ϰ such that: (a) the pair F′, s′ hasnot yet been considered by the algorithm, and (b) |F′| + |s′| is minimalamong such pairs;
 6. If no such pair F′, s′ exists, then return ⊥ andterminate;
 7. F := F′; s := s′; Repeat from step
 4.


16. The system of claim 10, wherein the query and the sources ofinformation are in a temporally-tagged logical representation form.